Sylowtételek

Sylowtételek, also known as Sylow's theorems, are a set of three important theorems in group theory, named after the Norwegian mathematician Ludwig Sylow. These theorems provide a powerful tool for analyzing the structure of finite groups. The first theorem states that for any prime number p and any finite group G, there exists a subgroup of G whose order is a power of p and which is divisible by p^k for some k. The second theorem asserts that the number of such subgroups is congruent to 1 modulo p. The third theorem states that any two such subgroups are conjugate within the group G. These theorems are fundamental in the study of finite groups and have numerous applications in various areas of mathematics and theoretical computer science.